How to do retopology?
Maybe you don't say enough about what your object looks like. Also, retopology is not the same as simplifying a mesh with deleting edge loops etc. But if you're talking about retopology, here is the basic way to begin in my opinion:


Create a plane over the high-poly object you are supposed to retopologize. This plane will be your low-poly version.





If your high-poly is symmetrical, give your low-poly a Mirror modifier. Enable the Clipping option.





On the horizontal menu bar, disable the Limit Selection to Visible option, enable the Snap, choose the Face mode, enable all the snap options.





Begin to move the vertices of your plane, you'll see that they will stick to the high-poly surface. Extrude edges, try to follow the main shapes and angles of the high-poly. About good topology and topology tricks, you can find some good advices here, it would take too long to summarize everything here.